Near-factorial experiments in nested row-column designs regulating efficiencies

We propose a method for constructing a nested row-column design d0, involving a control treatment and v test treatments, starting from a Youden or Latin square T and an incomplete block design d. It is shown how the choice of T and d regulates the efficiency factors of d0. Special attention is given to the case when the v test treatments have a factorial structure, and for appropriately chosen d, an admissibility property of d0, among all comparable designs, is established. Illustrative examples are given.